What is the discriminant of #-x^2+10x-56=-4x-7#?

1 Answer
Jul 27, 2015

Answer:

For this quadratic, #Delta = 0#.

Explanation:

In order to determine the determinant of this quadratic equation, you must first get it to quadratic form, which is

#ax^2 + bx + c = 0#

For this general form, the determinant is equal to

#Delta = b^2 - 4 * a * c#

So, to get your equation to mthis form, add #4x + 7# to both sides of the equation

#-x^2 + 10x - 56 + (4x + 7) = -color(red)(cancel(color(black)(4x))) - color(red)(cancel(color(black)(-7))) + color(red)(cancel(color(black)(4x))) + color(red)(cancel(color(black)(7)))#

#-x^2 + 14x - 49 = 0#

Now identify what the values for #a#, #b#, and #c# are. In your case,

#{(a = -1), (b=14), (c=-49) :}#

This means that the discriminant will be equal to

#Delta = 14^2 - 4 * (-1) * (-49)#

#Delta = 196 - 196 = color(green)(0)#

This means that your equation has only one real root

#x_(1,2) = (-b +- sqrt(Delta))/(2a)#

#x = (-b +- sqrt(0))/(2a) = color(blue)(-b/(2a))#

In your case, this solution is

#x = (-14)/(2 * (-1)) = 7#